Fast Principal Component Analysis for Cryo-EM Images

TL;DR

This paper presents a novel, fast PCA method for cryo-EM images that efficiently handles contrast transfer functions, significantly accelerating analysis of large datasets.

Contribution

A new Fourier-Bessel basis expansion algorithm enables rapid PCA computation for cryo-EM images, independent of contrast transfer function variations.

Findings

Achieves up to 100x speedup in PCA computation

Handles large cryo-EM datasets efficiently

Independent of contrast transfer function diversity

Abstract

Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-electron microscopy projection images that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For $N$ images of size $L\times L$, our method has time complexity $O(N L^3 + L^4)$ and space complexity $O(NL^2 + L^3)$. In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.